We want to run an application "silently (another user can be logged in on a desktop session)" on about 150 computers 24h/7. They all run Debian. We want to achieve this in Java. Application will be killed under some conditions. We want to automatically restart the application. We only have user rights, so we can't install it as a service.

Details:
We want to run an application on every computer that waits for tasks to run.
Problem:

if a process occupies too much processor time it will be killed.

after 7 days every process is killed.

Some computers don't run 24h/7 and do shutdown at night.st

Goal: How to run an application on 150 computers and automatically start the application again, if it is shutdown?

My idea: The computers are server and clients for tcp connections and send alive packets. If computer B doesn't get an alive message from A within a time period, it will restart the application at computer A.

Problem of my idea:
150x149 alive messages is too much traffic, even so it's Gigabit LAN.

idea 2:
They share the same disk. We can create a folder for just this application to access. But i rather don't like to write in a file the machine name of the server, and if the server crashes the first one that realizes this writes his machine name into it, if it's not the server's machine name. All others will look into this file, if they can't connect to the server.